^{1}

^{*}

^{2}

^{3}

^{1}

^{2}

^{3}

Edited by: Dimitrios Kraniotis, OsloMet - Oslo Metropolitan University, Norway

Reviewed by: Ying Hei Chui, University of Alberta, Canada; George Wardeh, Universit de Cergy-Pontoise, France

This article was submitted to Sustainable Design and Construction, a section of the journal Frontiers in Built Environment

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Cross Laminated Timber (CLT) is a relatively new timber product used in construction that has gained popularity over the last decade. The product itself is constituted by multiple glued layers of juxtaposed boards, usually arranged in an orthogonal direction between one layer and the adjacent ones. This particular structure brings several benefits, such as the possibility to use the same product both for walls and slabs, since it can bear in-plane and out-of-plane loads. However, the mechanical behavior differs from usual timber products, and research is still ongoing to achieve common agreement on standard procedures for testing products and theories for evaluating stresses for safety verifications. This paper focuses on the in-plane shear behavior of CLT and analyzes the existing methods to evaluate shear stresses. An experimental part then presents a four-point bending test of CLT beams with a specific geometry to induce shear failure. Results are reported both for the elastic range test, measuring the Modulus of Elasticity, and for the failure test to investigate shear behavior with regard to different mechanisms. Previously exposed methods are used for the calculation of shear stresses and to analyze the correspondence between them, and the results are then compared with other existing tests and values in literature. A new test setup for future research is eventually proposed.

Cross Laminated Timber is one of the many systems of building with timber, and it can be seen as a development of glued laminated timber by applying a similar concept on 2D elements instead of linear elements and with a new layup; its employment in construction is recent and it has become widely used mostly in Europe over the past 15 years. This product is usually produced in a plate-like shape and its alternated orthogonal board layer structure makes it apt to bear loads in and out of plane; hence the great benefit given by the possibility to use the same element both as a wall and as a floor slab. Another big advantage of this building system is the high degree of prefabrication it offers; this means more control during the production process, which translates to small tolerances. CLT is produced and, if necessary, cut in personalized shapes directly at the production site using CNC machines. Regarding the building site, this also means faster times and cleaner area, since the elements only need to be assembled and connected to each other to constitute the load-bearing structure of the building; it further permits faster application of additional insulation layers and finishes (see Brandner et al.,

The experimental campaign investigated a total number of 10 CLT beams, coming from different producers. The beams were cut from bigger panels and geometry was modified from the prescriptions of EN 408 (_{CL} = 600mm, the thickness varied depending on the number of layers and the producer, as seen in

Characteristics of tested CLT beams.

_{l,mean} [mm] |
_{CL} [mm] |
_{i} [mm] |
|||
---|---|---|---|---|---|

A3 | 4 | 100 | 90 | 30-30-30 | Yes |

A5 | 2 | 100 | 130 | 29-21-29-21-29 | Yes |

B5 | 2 | 80 | 135 | 27-27-27-27-27 | No |

C5 | 2 | 150 | 144 | 34-21-34-21-34 | No |

Tested specimen: for each series of specimen an image is provided showing the layup in the thickness direction and underlining differences.

The beams were tested using a four point bending test in accordance to the procedures of EN 408 (_{max,est} to obtain the load/displacement curve in order to calculate the modulus of elasticity. The load was applied by a hydraulic actuator, and the integrated load cell was used to measure the force. A rigid steel beam was used to distribute equally the load in two centered points at a distance _{1} = 800mm, _{1} = 600mm only for the first two specimen of series A3) while the fourth measured relative displacement.

Test setup presented in EN 408.

The modulus of elasticity was calculated in accordance with EN 408 (_{max} and 0,4 _{max} with a minimum correlation coefficient of 0,99 (the line must at least include the interval between 0,2 _{max} and 0,3 _{max}). The equation used is the following:

(_{2} − _{1}): load increase [N]

(_{2} − _{1}): displacement increase in the corresponding interval [mm]

_{1}: reference length for MoE determination [mm]

_{net}: moment of inertia referred to net section of the beam (layers parallel to ^{4}].

In this section various methods for calculating in-plane shear stresses will be presented and compared: a method based on the equilibrium, developed by Andreolli et al. (_{CL} of the beam), _{CL} of the beam. The shear force is expressed as force per unit length and for rotational equilibrium:

The layers oriented as the _{1}_{3}_{5}, while the layers oriented as the _{2}_{4}. The width of the laminations _{l} is assumed to be equal for boards oriented in both directions, if cracks are present or it is not constant for each board then _{l,mean} is to be used (unless otherwise specified).

Shear stresses, modified from COST document (Brandner et al.,

This method is based on equilibrium equations for each layer and glued interfaces and was presented in Andreolli et al. (

Shear stresses for the equilibrium method.

Shear stresses τ_{xy} and τ_{yx} are calculated using the thicknesses of the layers oriented as the respective direction:

For panels with symmetric layup _{1} = _{3} the stress τ_{yx} can be expressed as a function of τ_{xy}:

The global equilibrium to rotation poses:

At each glued interface, for action reaction:

Rotational equilibrium is calculated for each layer:

So, considering that τ_{xy1} = τ_{xy3} = τ_{xy} and τ_{yx2} = τ_{yx}, and using the relations previously found, the following can be obtained:

It is then possible to evaluate torsional shear stresses as a function of τ_{xy} considering that

Shear stresses τ_{xy} and τ_{yx} are calculated using the thicknesses of the layers oriented as the respective direction:

For panels with symmetric layup _{1} = _{3} = _{5} and _{2} = _{4} the stress τ_{yx} can be expressed as a function of τ_{xy}:

Similarly to the previous 3 layer case the same calculations are done, arriving at:

It is then possible to evaluate torsional shear stresses as a function of τ_{xy} considering that

So, differently from the case of a 3 layer panel torsional shear stresses are not equal for all glued interfaces but are major on external ones.

This model is developed by referring to an ideal CLT panel with an infinite number of layers and considering a crossing interface with width equal to the width of the laminations, see Bogensperger et al. (_{0} distributed on its entire thickness

This stress can be considered as the composition of two parts: an effective shear stress on the cross section with orientation perpendicular to grain

and a torsional shear stress

Since the real CLT panel has a finite number of layers it is necessary to refer to fictitious thicknesses of RVSE _{CA} = _{lay} − 1 is the number of glued interfaces):

So for a real CLT panel we get:

It can be seen that _{yx} for “usual” cases of symmetrical CLT panels with an odd number of layers and where the total thickness _{x} of layers oriented as _{y} of the other layers oriented as

Shear stresses for RVSE model.

This method was developed in Flaig and Blass (

And for a 5 layer panel:

With this method then the shear stresses are exactly the same as the Equilibrium method (except for the 0,20 reduction factor in the COST document). Torsional shear stresses are calculated as:

where _{xy} is the applied shear force, _{CA} = _{lay} − 1 is the number of glued interfaces, _{l} values they coincide, for the limit case of indeed

Remembering Equations (19) and (21) and with the consideration that

Two additional shear stresses on the glued interface are presented in this method, as seen in _{zx} which lies in the intersection plane (z) and is parallel to the axis of the beam (x), and τ_{zy}, which lies in the same plane and is parallel to the axis of the beam height (y):

Shear stresses for the beam method, on the right part a representative glue interface is shown.

The Austrian Annex K to

which then yields, with the previous conventions:

In this case then, these values are exactly the same as the previous methods. For what regards torsional shear stresses the proposed formulation is (adopting the previous conventions, where for usual panels the major shear stress is τ_{yx}):

The formula can be developed for a comparison:

Equilibrium method

The two formulations are similar, but the results obtained are quite different: one considers the maximum lamination thickness and the other the mean, and even when the these two values coincide (i.e., when all layers have equal thickness) the Austrian formulation gives values which are exactly double those of the equilibrium method.

Regarding bending stresses there is common agreement on the method of calculation, so with the usual convention of

_{net}: moment of inertia referret to net section of the beam (layers parallel to ^{4}]

_{CL}: height of the CLT beam [mm].

In

Modulus of Elasticity values [GPa].

A3 | – | – | 12,298 | 10,997 | 11,648 |

A5 | 15,845 | 14,758 | – | – | 15,302 |

B5 | 14,445 | 16,661 | – | – | 15,553 |

C5 | 12,493 | 10,775 | – | – | 11,634 |

The results regarding failure are instead presented in _{max} = _{xy} and _{max} = _{xz}.

Values of applied force and relative shear and bending moment at failure.

A3 | 313 | 324 | 372 | 310 | 330 | 165 | 128 |

A5 | 506 | 515 | – | – | 511 | 255 | 179 |

B5 | 417 | 405 | – | – | 411 | 206 | 144 |

C5 | 565 | 495 | – | – | 530 | 265 | 186 |

The result in terms of bending and shear stresses are presented in

Stresses at failure, shear stresses calculated with the equilibrium method.

_{m,edge,x} |
_{xy} |
_{yx} |
_{T,ext} |
_{T,int} |
||
---|---|---|---|---|---|---|

A3 | 35,42 | 6,88 | 13,75 | 6,19 | / | Torsional |

A5 | 34,20 | 7,34 | 15,21 | 6,39 | 3,19 | Torsional |

B5 | 29,59 | 6,34 | 9,51 | 6,42 | 3,21 | Torsional |

C5 | 30,31 | 6,50 | 15,77 | 4,42 | 2,21 | Bending |

It is also interesting to see from _{xy} is the same value for all methods, except for the COST method, which results in a slightly higher value due to a 0,20 reduction factor for the thickness of outer layers. Shear stress τ_{yx} is the same value for all methods, while torsional shear stresses present some differences. The equilibrium method presents two different values, one for external and one for internal interfaces while the other methods present a single value which for the RVSE, COST and Beam methods is more or less the average of the previous values, while for the Austrian Annex the value is much higher.

Comparison of shear stresses at failure. Note that for the RVSE method there is no value for τ_{xy} since this method only provides the value of major stress τ_{yx}. Note also that for 5 layer panels the equilibrium method provides two values of τ_{T}, one for the external and one for the internal glued interface.

The different failures for the four types of specimen can be seen in

Failure modes.

A comparison can be done with stress values from other authors present in the literature. Regarding bending stresses at failure a value _{m,mean} = 38, 5MPa was obtained in Jöbstl et al. (_{v,mean} = 12, 8MPa, which is lower (except for B5 series) than the values obtained here. Two considerations can be done: the first is that, in the present testing campaign, shear failure in the lamellas was not obtained. The second is that the test devised in Wallner (_{v,mean} = 9MPa. Another test which succeeded in obtaining shear failure in lamellas is the one presented in Brandner et al. (_{v,mean} = 7, 3MPa and _{v,mean} = 7, 6MPa. Regarding torsional stresses, the majority of tests found in the literature are on a single crossing interface, such as the ones present in Blaß and Görlacher (_{t,mean} = 3, 6MPa and _{t,mean} = 3, 5MPa, which are well below the values obtained in the present article. This suggests probably that torsional shear strength is much higher in real scale CLT panels, which implies that torsional tests on single nodes may not be representative of the complexity of a complete CLT panel. It is also worth noting that in this paper a Jourawski shear stress distribution was assumed, thus the 1, 5 factor may imply an overestimation of real stress distribution, both for shear stresses in the lamellas and for torsional shear stresses at the glue interface.

In-plane shear stresses for CLT remain an open topic regarding which method to use for their evaluation and the test setup to measure strength values. This is due to the particular structure of this timber product which, differently from other simpler products like solid wood and GLT, presents different types of failure depending on loading, geometry and layup. In this paper a review and comparison between the available methods to calculate in-plane shear stresses for CLT panels was presented, with particular effort directed at trying to make uniform the notation for all methods to match the one of

A four-point bending test was then applied to four different types of CLT beams to investigate in-plane shear behavior; in spite of the specifically chosen geometry no shear failure in the laminations was obtained—only torsional shear failure and bending failure in one case, which highlighted the inapplicability of such a testing setup to obtain information about shear strength. It is then necessary to devise a specific test capable of singling out the shear failure in laminations, and promising first results are coming from a test setup based on the diagonal compression of a CLT panel which will be presented in a future paper. Nevertheless, the high values of torsional shear stresses obtained at failure in this paper indicate much higher strength than the values present nowadays in the literature, underlying the importance of testing full-scale CLT panels and not simply conducting torsional tests on single nodes or crossing interfaces, even though this is presently still suggested in EN 16351 (

The datasets generated for this study are available on request to the corresponding author.

MA, RT, and FB contributed conception and design of the study. MA performed the testing campaign. FB wrote the first draft of the manuscript. RT, MA, and FB wrote sections of the manuscript. All authors contributed to manuscript revision, read and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

For a 3 layer panel _{lay} denotes the total number of layers, _{lay, x} is the number of layers with grain oriented in the x direction, _{l,x} is the thickness of a single lamination oriented in the x direction):

Equilibrium method

RVSE method

For a 5 layer panels:

Equilibrium method

RVSE method

So for CLT panels (with an odd number of layers) where the layers oriented in the

Keeping the same hypothesis made regarding shear stresses it is possible to compare torsional shear stresses. It can be seen that for a 3 layer panels it is the same value for both methods, while for a 5 layer panel a constant value is obtained from the RVSE method which is the average of the previous internal and external values of equilibrium method.

Equilibrium method

RVSE method

For 5 layer panel Equilibrium method

RVSE method

The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.

σ_{m,edge,x} |
in plane bending stresses, referred to layers parallel to the grain of the outermost layers (x-direction) |

σ_{m,edge,y} |
in plane bending stresses, referred to layers perpendicular to the grain of the outermost layers (y-direction) |

σ_{c,x} |
compression stresses, referred to layers parallel to the grain of the outermost layers (x-direction) |

σ_{c,y} |
compression stresses, referred to layers perpendicular to the grain of the outermost layers (y-direction) |

σ_{m,x} |
out of plane bending stresses, referred to layers parallel to the grain of the outermost layers (x-direction) |

σ_{m,y} |
out of plane bending stresses, referred to layers perpendicular to the grain of the outermost layers (y-direction) |

σ_{t,x} |
tensile stresses, referred to layers parallel to the grain of the outermost layers (x-direction) |

σ_{t,y} |
tensile stresses, referred to layers perpendicular to the grain of the outermost layers (y-direction) |

σ_{xy} |
in plane shear stresses stresses, referred to layers parallel to the grain of the outermost layers (x-direction) |

σ_{xz} |
out of plane shear stresses stresses, referred to layers parallel to the grain of the outermost layers (x-direction) |

τ_{0} |
nominal shear stress (RVSE method) |

nominal shear stress, referred to real panel (RVSE method) | |

τ_{v} |
effective shear stress (RVSE method) |

effective shear stress, referred to real panel (RVSE method) | |

τ_{T,ext} |
torsional stresses at glue interface, referred to external interfaces (Equilibrium method) |

τ_{T,int} |
torsional stresses at glue interface, referred to internal interfaces (Equilibrium method) |

τ_{T} |
torsional stresses at glue interface |

τ_{yx} |
in plane shear stresses, referred to layers perpendicular to the grain of the outermost layers (y-direction) |

τ_{yz} |
out of plane shear stresses, referred to layers perpendicular to the grain of the outermost layers (y-direction) |

_{l} |
width of laminations or mean distance between the edge and a groove or mean spacing between grooves within a lamination |

_{l,mean} |
mean width of laminations or mean distance between the edge and a groove or mean spacing between grooves within a lamination |

force | |

_{max,est} |
estimated maximum force at failure |

_{max} |
maximum force at failure |

_{CL} |
cross laminated timber height |

_{net} |
moment of inertia referred to net section |

length or span | |

bending moment | |

bending moment per unit length | |

_{T} |
torsional moment at glued interface |

tension/compression force per unit length | |

_{l} |
number of laminations in the height of the beam |

_{lay,x} |
number of layers in a cross laminated timber member with grain parallel to x-direction |

_{lay,y} |
number of layers in a cross laminated timber member with grain parallel to y-direction |

_{lay} |
number of layers of cross laminated timber member |

_{CA} |
number of glued interfaces |

_{1}_{3}_{5} |
thickness of each lamination parallel to the grain of outermost layers (x-direction) |

_{2}_{4} |
thickness of each lamination perpendicular to the grain of outermost layers (y-direction) |

_{i} |
thickness of a single lamination |

fictitious thickness of a single lamination (RVSE method) | |

_{x} |
sum of thicknesses of layers in x-direction |

_{y} |
sum of thicknesses of layers in y-direction |

_{CL} |
cross laminated timber thickness |

_{l,x} |
equal thickness of each layer in a cross laminated timber member with grain parallel to x-direction (_{l,x} = _{1} = _{3} = _{5}) |

_{l,y} |
equal thickness of each layer in a cross laminated timber member with grain parallel to y-direction (_{l,y} = _{2} = _{4}) |

shear force | |

shear force per unit length | |

torsional resistance moment |